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opensimplexnoise.js
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/*
* OpenSimplex Noise in Java.
* by Kurt Spencer
*
* v1.1 (October 5, 2014)
* - Added 2D and 4D implementations.
* - Proper gradient sets for all dimensions, from a
* dimensionally-generalizable scheme with an actual
* rhyme and reason behind it.
* - Removed default permutation array in favor of
* default seed.
* - Changed seed-based constructor to be independent
* of any particular randomization library, so results
* will be the same when ported to other languages.
*
* Adaptation for P5.js by Gregory Jarrige (April 2, 2018)
*/
class OpenSimplexNoise {
constructor(perm = 0) {
this.STRETCH_CONSTANT_2D = -0.211324865405187; //(1/Math.sqrt(2+1)-1)/2;
this.SQUISH_CONSTANT_2D = 0.366025403784439; //(Math.sqrt(2+1)-1)/2;
this.STRETCH_CONSTANT_3D = -1.0 / 6; //(1/Math.sqrt(3+1)-1)/3;
this.SQUISH_CONSTANT_3D = 1.0 / 3; //(Math.sqrt(3+1)-1)/3;
this.STRETCH_CONSTANT_4D = -0.138196601125011; //(1/Math.sqrt(4+1)-1)/4;
this.SQUISH_CONSTANT_4D = 0.309016994374947; //(Math.sqrt(4+1)-1)/4;
this.NORM_CONSTANT_2D = 47;
this.NORM_CONSTANT_3D = 103;
this.NORM_CONSTANT_4D = 30;
this.DEFAULT_SEED = 0;
this.perm = [];
this.permGradIndex3D = [];
//Gradients for 2D. They approximate the directions to the
//vertices of an octagon from the center.
this.gradients2D = new Array(
5, 2, 2, 5,
-5, 2, -2, 5,
5, -2, 2, -5,
-5, -2, -2, -5,
);
//Gradients for 3D. They approximate the directions to the
//vertices of a rhombicuboctahedron from the center, skewed so
//that the triangular and square facets can be inscribed inside
//circles of the same radius.
this.gradients3D = new Array(
-11, 4, 4, -4, 11, 4, -4, 4, 11,
11, 4, 4, 4, 11, 4, 4, 4, 11,
-11, -4, 4, -4, -11, 4, -4, -4, 11,
11, -4, 4, 4, -11, 4, 4, -4, 11,
-11, 4, -4, -4, 11, -4, -4, 4, -11,
11, 4, -4, 4, 11, -4, 4, 4, -11,
-11, -4, -4, -4, -11, -4, -4, -4, -11,
11, -4, -4, 4, -11, -4, 4, -4, -11,
);
//Gradients for 4D. They approximate the directions to the
//vertices of a disprismatotesseractihexadecachoron from the center,
//skewed so that the tetrahedral and cubic facets can be inscribed inside
//spheres of the same radius.
this.gradients4D = new Array(
3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3,
-3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3,
3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3,
-3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3,
3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3,
-3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3,
3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3,
-3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3,
3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3,
-3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3,
3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3,
-3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3,
3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3,
-3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3,
3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3,
-3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3,
);
}
config(param) {
if (Object.prototype.toString.call(param) === '[object Array]') {
if (param.length < 256) {
console.log('parameter of config method must contain at leas 256 items');
return;
}
for (let i = 0; i < 256; i++) {
//Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array.
this.permGradIndex3D[i] = (this.perm[i] % (this.gradients3D.length / 3)) * 3;
}
return;
}
if (Object.prototype.toString.call(param) === '[object Number]') {
//Initializes the class using a permutation array generated from a 64-bit seed.
//Generates a proper permutation (i.e. doesn't merely perform N successive pair swaps on a base array)
//Uses a simple 64-bit LCG.
if (param === 0) {
console.log('parameter of config method must be different of zero');
return;
}
var seed = param;
this.perm = new Array(256);
this.permGradIndex3D = new Array(256);
var source = new Array(256);
for (let i = 0; i < 256; i++) {
source[i] = i;
}
seed = seed * 6364136223846793005 + 1442695040888963407;
seed = seed * 6364136223846793005 + 1442695040888963407;
seed = seed * 6364136223846793005 + 1442695040888963407;
for (let i = 255; i >= 0; i--) {
seed = seed * 6364136223846793005 + 1442695040888963407;
var r = int((seed + 31) % (i + 1));
if (r < 0) {
r += (i + 1);
}
this.perm[i] = source[r];
this.permGradIndex3D[i] = (this.perm[i] % (this.gradients3D.length / 3)) * 3;
source[r] = source[i];
}
return;
}
}
//2D OpenSimplex Noise.
eval2(x, y) {
//Place input coordinates onto grid.
var stretchOffset = (x + y) * this.STRETCH_CONSTANT_2D;
var xs = x + stretchOffset;
var ys = y + stretchOffset;
//Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
var xsb = this.fastFloor(xs);
var ysb = this.fastFloor(ys);
//Skew out to get actual coordinates of rhombus origin. We'll need these later.
var squishOffset = (xsb + ysb) * this.SQUISH_CONSTANT_2D;
var xb = xsb + squishOffset;
var yb = ysb + squishOffset;
//Compute grid coordinates relative to rhombus origin.
var xins = xs - xsb;
var yins = ys - ysb;
//Sum those together to get a value that determines which region we're in.
var inSum = xins + yins;
//Positions relative to origin point.
var dx0 = x - xb;
var dy0 = y - yb;
//We'll be defining these inside the next block and using them afterwards.
var dx_ext, dy_ext;
var xsv_ext, ysv_ext;
var value = 0;
//Contribution (1,0)
var dx1 = dx0 - 1 - this.SQUISH_CONSTANT_2D;
var dy1 = dy0 - 0 - this.SQUISH_CONSTANT_2D;
var attn1 = 2 - dx1 * dx1 - dy1 * dy1;
if (attn1 > 0) {
attn1 *= attn1;
value += attn1 * attn1 * this.extrapolate4(xsb + 1, ysb + 0, dx1, dy1);
}
//Contribution (0,1)
var dx2 = dx0 - 0 - this.SQUISH_CONSTANT_2D;
var dy2 = dy0 - 1 - this.SQUISH_CONSTANT_2D;
var attn2 = 2 - dx2 * dx2 - dy2 * dy2;
if (attn2 > 0) {
attn2 *= attn2;
value += attn2 * attn2 * this.extrapolate4(xsb + 0, ysb + 1, dx2, dy2);
}
if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0)
var zins = 1 - inSum;
if (zins > xins || zins > yins) { //(0,0) is one of the closest two triangular vertices
if (xins > yins) {
xsv_ext = xsb + 1;
ysv_ext = ysb - 1;
dx_ext = dx0 - 1;
dy_ext = dy0 + 1;
} else {
xsv_ext = xsb - 1;
ysv_ext = ysb + 1;
dx_ext = dx0 + 1;
dy_ext = dy0 - 1;
}
} else { //(1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1;
ysv_ext = ysb + 1;
dx_ext = dx0 - 1 - 2 * this.SQUISH_CONSTANT_2D;
dy_ext = dy0 - 1 - 2 * this.SQUISH_CONSTANT_2D;
}
} else { //We're inside the triangle (2-Simplex) at (1,1)
var zins = 2 - inSum;
if (zins < xins || zins < yins) { //(0,0) is one of the closest two triangular vertices
if (xins > yins) {
xsv_ext = xsb + 2;
ysv_ext = ysb + 0;
dx_ext = dx0 - 2 - 2 * this.SQUISH_CONSTANT_2D;
dy_ext = dy0 + 0 - 2 * this.SQUISH_CONSTANT_2D;
} else {
xsv_ext = xsb + 0;
ysv_ext = ysb + 2;
dx_ext = dx0 + 0 - 2 * this.SQUISH_CONSTANT_2D;
dy_ext = dy0 - 2 - 2 * this.SQUISH_CONSTANT_2D;
}
} else { //(1,0) and (0,1) are the closest two vertices.
dx_ext = dx0;
dy_ext = dy0;
xsv_ext = xsb;
ysv_ext = ysb;
}
xsb += 1;
ysb += 1;
dx0 = dx0 - 1 - 2 * this.SQUISH_CONSTANT_2D;
dy0 = dy0 - 1 - 2 * this.SQUISH_CONSTANT_2D;
}
//Contribution (0,0) or (1,1)
var attn0 = 2 - dx0 * dx0 - dy0 * dy0;
if (attn0 > 0) {
attn0 *= attn0;
value += attn0 * attn0 * this.extrapolate4(xsb, ysb, dx0, dy0);
}
//Extra Vertex
var attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
if (attn_ext > 0) {
attn_ext *= attn_ext;
value += attn_ext * attn_ext * this.extrapolate4(xsv_ext, ysv_ext, dx_ext, dy_ext);
}
return value / this.NORM_CONSTANT_2D;
}
//3D OpenSimplex Noise.
eval3(x, y, z) {
//Place input coordinates on simplectic honeycomb.
var stretchOffset = (x + y + z) * this.STRETCH_CONSTANT_3D;
var xs = x + stretchOffset;
var ys = y + stretchOffset;
var zs = z + stretchOffset;
//Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
var xsb = this.fastFloor(xs);
var ysb = this.fastFloor(ys);
var zsb = this.fastFloor(zs);
//Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
var squishOffset = (xsb + ysb + zsb) * this.SQUISH_CONSTANT_3D;
var xb = xsb + squishOffset;
var yb = ysb + squishOffset;
var zb = zsb + squishOffset;
//Compute simplectic honeycomb coordinates relative to rhombohedral origin.
var xins = xs - xsb;
var yins = ys - ysb;
var zins = zs - zsb;
//Sum those together to get a value that determines which region we're in.
var inSum = xins + yins + zins;
//Positions relative to origin point.
var dx0 = x - xb;
var dy0 = y - yb;
var dz0 = z - zb;
//We'll be defining these inside the next block and using them afterwards.
var dx_ext0, dy_ext0, dz_ext0;
var dx_ext1, dy_ext1, dz_ext1;
var xsv_ext0, ysv_ext0, zsv_ext0;
var xsv_ext1, ysv_ext1, zsv_ext1;
var value = 0;
if (inSum <= 1) { //We're inside the tetrahedron (3-Simplex) at (0,0,0)
//Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest.
var aPovar = 0x01;
var aScore = xins;
var bPovar = 0x02;
var bScore = yins;
if (aScore >= bScore && zins > bScore) {
bScore = zins;
bPovar = 0x04;
} else if (aScore < bScore && zins > aScore) {
aScore = zins;
aPovar = 0x04;
}
//Now we determine the two lattice points not part of the tetrahedron that may contribute.
//This depends on the closest two tetrahedral vertices, including (0,0,0)
var wins = 1 - inSum;
if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices.
var c = (bScore > aScore ? bPovar : aPoint); //Our other closest vertex is the closest out of a and b.
if ((c & 0x01) == 0) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsb;
dx_ext0 = dx0 + 1;
dx_ext1 = dx0;
} else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx_ext1 = dx0 - 1;
}
if ((c & 0x02) == 0) {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0;
if ((c & 0x01) == 0) {
ysv_ext1 -= 1;
dy_ext1 += 1;
} else {
ysv_ext0 -= 1;
dy_ext0 += 1;
}
} else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - 1;
}
if ((c & 0x04) == 0) {
zsv_ext0 = zsb;
zsv_ext1 = zsb - 1;
dz_ext0 = dz0;
dz_ext1 = dz0 + 1;
} else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - 1;
}
} else { //(0,0,0) is not one of the closest two tetrahedral vertices.
var c = (byte)(aPovar | bPoint); //Our two extra vertices are determined by the closest two.
if ((c & 0x01) == 0) {
xsv_ext0 = xsb;
xsv_ext1 = xsb - 1;
dx_ext0 = dx0 - 2 * this.SQUISH_CONSTANT_3D;
dx_ext1 = dx0 + 1 - this.SQUISH_CONSTANT_3D;
} else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
dx_ext1 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
}
if ((c & 0x02) == 0) {
ysv_ext0 = ysb;
ysv_ext1 = ysb - 1;
dy_ext0 = dy0 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 + 1 - this.SQUISH_CONSTANT_3D;
} else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
}
if ((c & 0x04) == 0) {
zsv_ext0 = zsb;
zsv_ext1 = zsb - 1;
dz_ext0 = dz0 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 + 1 - this.SQUISH_CONSTANT_3D;
} else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
}
}
//Contribution (0,0,0)
var attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
if (attn0 > 0) {
attn0 *= attn0;
value += attn0 * attn0 * this.extrapolate6(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0);
}
//Contribution (1,0,0)
var dx1 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
var dy1 = dy0 - 0 - this.SQUISH_CONSTANT_3D;
var dz1 = dz0 - 0 - this.SQUISH_CONSTANT_3D;
var attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
if (attn1 > 0) {
attn1 *= attn1;
value += attn1 * attn1 * this.extrapolate6(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
}
//Contribution (0,1,0)
var dx2 = dx0 - 0 - this.SQUISH_CONSTANT_3D;
var dy2 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
var dz2 = dz1;
var attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
if (attn2 > 0) {
attn2 *= attn2;
value += attn2 * attn2 * this.extrapolate6(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
}
//Contribution (0,0,1)
var dx3 = dx2;
var dy3 = dy1;
var dz3 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
var attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
if (attn3 > 0) {
attn3 *= attn3;
value += attn3 * attn3 * this.extrapolate6(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
}
} else if (inSum >= 2) { //We're inside the tetrahedron (3-Simplex) at (1,1,1)
//Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1).
var aPovar = 0x06;
var aScore = xins;
var bPovar = 0x05;
var bScore = yins;
if (aScore <= bScore && zins < bScore) {
bScore = zins;
bPovar = 0x03;
} else if (aScore > bScore && zins < aScore) {
aScore = zins;
aPovar = 0x03;
}
//Now we determine the two lattice points not part of the tetrahedron that may contribute.
//This depends on the closest two tetrahedral vertices, including (1,1,1)
var wins = 3 - inSum;
if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices.
var c = (bScore < aScore ? bPovar : aPoint); //Our other closest vertex is the closest out of a and b.
if ((c & 0x01) != 0) {
xsv_ext0 = xsb + 2;
xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - 2 - 3 * this.SQUISH_CONSTANT_3D;
dx_ext1 = dx0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
} else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx_ext1 = dx0 - 3 * this.SQUISH_CONSTANT_3D;
}
if ((c & 0x02) != 0) {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
if ((c & 0x01) != 0) {
ysv_ext1 += 1;
dy_ext1 -= 1;
} else {
ysv_ext0 += 1;
dy_ext0 -= 1;
}
} else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - 3 * this.SQUISH_CONSTANT_3D;
}
if ((c & 0x04) != 0) {
zsv_ext0 = zsb + 1;
zsv_ext1 = zsb + 2;
dz_ext0 = dz0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 - 3 * this.SQUISH_CONSTANT_3D;
} else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - 3 * this.SQUISH_CONSTANT_3D;
}
} else { //(1,1,1) is not one of the closest two tetrahedral vertices.
var c = (byte)(aPovar & bPoint); //Our two extra vertices are determined by the closest two.
if ((c & 0x01) != 0) {
xsv_ext0 = xsb + 1;
xsv_ext1 = xsb + 2;
dx_ext0 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
dx_ext1 = dx0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
} else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx0 - this.SQUISH_CONSTANT_3D;
dx_ext1 = dx0 - 2 * this.SQUISH_CONSTANT_3D;
}
if ((c & 0x02) != 0) {
ysv_ext0 = ysb + 1;
ysv_ext1 = ysb + 2;
dy_ext0 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
} else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy0 - this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 * this.SQUISH_CONSTANT_3D;
}
if ((c & 0x04) != 0) {
zsv_ext0 = zsb + 1;
zsv_ext1 = zsb + 2;
dz_ext0 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
} else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz0 - this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 * this.SQUISH_CONSTANT_3D;
}
}
//Contribution (1,1,0)
var dx3 = dx0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var dy3 = dy0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var dz3 = dz0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
if (attn3 > 0) {
attn3 *= attn3;
value += attn3 * attn3 * this.extrapolate6(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3);
}
//Contribution (1,0,1)
var dx2 = dx3;
var dy2 = dy0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var dz2 = dz0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
if (attn2 > 0) {
attn2 *= attn2;
value += attn2 * attn2 * this.extrapolate6(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2);
}
//Contribution (0,1,1)
var dx1 = dx0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var dy1 = dy3;
var dz1 = dz2;
var attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
if (attn1 > 0) {
attn1 *= attn1;
value += attn1 * attn1 * this.extrapolate6(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1);
}
//Contribution (1,1,1)
dx0 = dx0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
dy0 = dy0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
dz0 = dz0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
var attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
if (attn0 > 0) {
attn0 *= attn0;
value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
}
} else { //We're inside the octahedron (Rectified 3-Simplex) in between.
var aScore;
var aPoint;
var aIsFurtherSide;
var bScore;
var bPoint;
var bIsFurtherSide;
//Decide between povar (0,0,1) and (1,1,0) as closest
var p1 = xins + yins;
if (p1 > 1) {
aScore = p1 - 1;
aPovar = 0x03;
aIsFurtherSide = true;
} else {
aScore = 1 - p1;
aPovar = 0x04;
aIsFurtherSide = false;
}
//Decide between povar (0,1,0) and (1,0,1) as closest
var p2 = xins + zins;
if (p2 > 1) {
bScore = p2 - 1;
bPovar = 0x05;
bIsFurtherSide = true;
} else {
bScore = 1 - p2;
bPovar = 0x02;
bIsFurtherSide = false;
}
//The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer.
var p3 = yins + zins;
if (p3 > 1) {
var score = p3 - 1;
if (aScore <= bScore && aScore < score) {
aScore = score;
aPovar = 0x06;
aIsFurtherSide = true;
} else if (aScore > bScore && bScore < score) {
bScore = score;
bPovar = 0x06;
bIsFurtherSide = true;
}
} else {
var score = 1 - p3;
if (aScore <= bScore && aScore < score) {
aScore = score;
aPovar = 0x01;
aIsFurtherSide = false;
} else if (aScore > bScore && bScore < score) {
bScore = score;
bPovar = 0x01;
bIsFurtherSide = false;
}
}
//Where each of the two closest points are determines how the extra two vertices are calculated.
if (aIsFurtherSide == bIsFurtherSide) {
if (aIsFurtherSide) { //Both closest points on (1,1,1) side
//One of the two extra points is (1,1,1)
dx_ext0 = dx0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
dy_ext0 = dy0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
dz_ext0 = dz0 - 1 - 3 * this.SQUISH_CONSTANT_3D;
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb + 1;
//Other extra povar is based on the shared axis.
var c = (byte)(aPovar & bPoint);
if ((c & 0x01) != 0) {
dx_ext1 = dx0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 * this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb + 2;
ysv_ext1 = ysb;
zsv_ext1 = zsb;
} else if ((c & 0x02) != 0) {
dx_ext1 = dx0 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 * this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb;
ysv_ext1 = ysb + 2;
zsv_ext1 = zsb;
} else {
dx_ext1 = dx0 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 - 2 * this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb;
ysv_ext1 = ysb;
zsv_ext1 = zsb + 2;
}
} else {//Both closest points on (0,0,0) side
//One of the two extra points is (0,0,0)
dx_ext0 = dx0;
dy_ext0 = dy0;
dz_ext0 = dz0;
xsv_ext0 = xsb;
ysv_ext0 = ysb;
zsv_ext0 = zsb;
//Other extra povar is based on the omitted axis.
var c = (byte)(aPovar | bPoint);
if ((c & 0x01) == 0) {
dx_ext1 = dx0 + 1 - this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb - 1;
ysv_ext1 = ysb + 1;
zsv_ext1 = zsb + 1;
} else if ((c & 0x02) == 0) {
dx_ext1 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 + 1 - this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb + 1;
ysv_ext1 = ysb - 1;
zsv_ext1 = zsb + 1;
} else {
dx_ext1 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 + 1 - this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb + 1;
ysv_ext1 = ysb + 1;
zsv_ext1 = zsb - 1;
}
}
} else { //One povar on (0,0,0) side, one povar on (1,1,1) side
var c1, c2;
if (aIsFurtherSide) {
c1 = aPoint;
c2 = bPoint;
} else {
c1 = bPoint;
c2 = aPoint;
}
//One contribution is a permutation of (1,1,-1)
if ((c1 & 0x01) == 0) {
dx_ext0 = dx0 + 1 - this.SQUISH_CONSTANT_3D;
dy_ext0 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
dz_ext0 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
xsv_ext0 = xsb - 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb + 1;
} else if ((c1 & 0x02) == 0) {
dx_ext0 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
dy_ext0 = dy0 + 1 - this.SQUISH_CONSTANT_3D;
dz_ext0 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb - 1;
zsv_ext0 = zsb + 1;
} else {
dx_ext0 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
dy_ext0 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
dz_ext0 = dz0 + 1 - this.SQUISH_CONSTANT_3D;
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb - 1;
}
//One contribution is a permutation of (0,0,2)
dx_ext1 = dx0 - 2 * this.SQUISH_CONSTANT_3D;
dy_ext1 = dy0 - 2 * this.SQUISH_CONSTANT_3D;
dz_ext1 = dz0 - 2 * this.SQUISH_CONSTANT_3D;
xsv_ext1 = xsb;
ysv_ext1 = ysb;
zsv_ext1 = zsb;
if ((c2 & 0x01) != 0) {
dx_ext1 -= 2;
xsv_ext1 += 2;
} else if ((c2 & 0x02) != 0) {
dy_ext1 -= 2;
ysv_ext1 += 2;
} else {
dz_ext1 -= 2;
zsv_ext1 += 2;
}
}
//Contribution (1,0,0)
var dx1 = dx0 - 1 - this.SQUISH_CONSTANT_3D;
var dy1 = dy0 - 0 - this.SQUISH_CONSTANT_3D;
var dz1 = dz0 - 0 - this.SQUISH_CONSTANT_3D;
var attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
if (attn1 > 0) {
attn1 *= attn1;
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
}
//Contribution (0,1,0)
var dx2 = dx0 - 0 - this.SQUISH_CONSTANT_3D;
var dy2 = dy0 - 1 - this.SQUISH_CONSTANT_3D;
var dz2 = dz1;
var attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
if (attn2 > 0) {
attn2 *= attn2;
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
}
//Contribution (0,0,1)
var dx3 = dx2;
var dy3 = dy1;
var dz3 = dz0 - 1 - this.SQUISH_CONSTANT_3D;
var attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
if (attn3 > 0) {
attn3 *= attn3;
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
}
//Contribution (1,1,0)
var dx4 = dx0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var dy4 = dy0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var dz4 = dz0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4;
if (attn4 > 0) {
attn4 *= attn4;
value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4);
}
//Contribution (1,0,1)
var dx5 = dx4;
var dy5 = dy0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var dz5 = dz0 - 1 - 2 * this.SQUISH_CONSTANT_3D;
var attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5;
if (attn5 > 0) {
attn5 *= attn5;
value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5);
}
//Contribution (0,1,1)
var dx6 = dx0 - 0 - 2 * this.SQUISH_CONSTANT_3D;
var dy6 = dy4;
var dz6 = dz5;
var attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6;
if (attn6 > 0) {
attn6 *= attn6;
value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6);
}
}
//First extra vertex
var attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0;
if (attn_ext0 > 0)
{
attn_ext0 *= attn_ext0;
value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0);
}
//Second extra vertex
var attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1;
if (attn_ext1 > 0)
{
attn_ext1 *= attn_ext1;
value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
}
return value / this.NORM_CONSTANT_3D;
}
//4D OpenSimplex Noise.
eval4(x, y, z, w) {
//Place input coordinates on simplectic honeycomb.
var stretchOffset = (x + y + z + w) * this.STRETCH_CONSTANT_4D;
var xs = x + stretchOffset;
var ys = y + stretchOffset;
var zs = z + stretchOffset;
var ws = w + stretchOffset;
//Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
var xsb = this.fastFloor(xs);
var ysb = this.fastFloor(ys);
var zsb = this.fastFloor(zs);
var wsb = this.fastFloor(ws);
//Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
var squishOffset = (xsb + ysb + zsb + wsb) * this.SQUISH_CONSTANT_4D;
var xb = xsb + squishOffset;
var yb = ysb + squishOffset;
var zb = zsb + squishOffset;
var wb = wsb + squishOffset;
//Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
var xins = xs - xsb;
var yins = ys - ysb;
var zins = zs - zsb;
var wins = ws - wsb;
//Sum those together to get a value that determines which region we're in.
var inSum = xins + yins + zins + wins;
//Positions relative to origin point.
var dx0 = x - xb;
var dy0 = y - yb;
var dz0 = z - zb;
var dw0 = w - wb;
//We'll be defining these inside the next block and using them afterwards.
var dx_ext0, dy_ext0, dz_ext0, dw_ext0;
var dx_ext1, dy_ext1, dz_ext1, dw_ext1;
var dx_ext2, dy_ext2, dz_ext2, dw_ext2;
var xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0;
var xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1;
var xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2;
var value = 0;
if (inSum <= 1) { //We're inside the pentachoron (4-Simplex) at (0,0,0,0)
//Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
var aPovar = 0x01;
var aScore = xins;
var bPovar = 0x02;
var bScore = yins;
if (aScore >= bScore && zins > bScore) {
bScore = zins;
bPovar = 0x04;
} else if (aScore < bScore && zins > aScore) {
aScore = zins;
aPovar = 0x04;
}
if (aScore >= bScore && wins > bScore) {
bScore = wins;
bPovar = 0x08;
} else if (aScore < bScore && wins > aScore) {
aScore = wins;
aPovar = 0x08;
}
//Now we determine the three lattice points not part of the pentachoron that may contribute.
//This depends on the closest two pentachoron vertices, including (0,0,0,0)
var uins = 1 - inSum;
if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices.
var c = (bScore > aScore ? bPovar : aPoint); //Our other closest vertex is the closest out of a and b.
if ((c & 0x01) == 0) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsv_ext2 = xsb;
dx_ext0 = dx0 + 1;
dx_ext1 = dx_ext2 = dx0;
} else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1;
}
if ((c & 0x02) == 0) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy_ext1 = dy_ext2 = dy0;
if ((c & 0x01) == 0x01) {
ysv_ext0 -= 1;
dy_ext0 += 1;
} else {
ysv_ext1 -= 1;
dy_ext1 += 1;
}
} else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1;
}
if ((c & 0x04) == 0) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz_ext1 = dz_ext2 = dz0;
if ((c & 0x03) != 0) {
if ((c & 0x03) == 0x03) {
zsv_ext0 -= 1;
dz_ext0 += 1;
} else {
zsv_ext1 -= 1;
dz_ext1 += 1;
}
} else {
zsv_ext2 -= 1;
dz_ext2 += 1;
}
} else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1;
}
if ((c & 0x08) == 0) {
wsv_ext0 = wsv_ext1 = wsb;
wsv_ext2 = wsb - 1;
dw_ext0 = dw_ext1 = dw0;
dw_ext2 = dw0 + 1;
} else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1;
}
} else { //(0,0,0,0) is not one of the closest two pentachoron vertices.
var c = (byte)(aPovar | bPoint); //Our three extra vertices are determined by the closest two.
if ((c & 0x01) == 0) {
xsv_ext0 = xsv_ext2 = xsb;
xsv_ext1 = xsb - 1;
dx_ext0 = dx0 - 2 * this.SQUISH_CONSTANT_4D;
dx_ext1 = dx0 + 1 - this.SQUISH_CONSTANT_4D;
dx_ext2 = dx0 - this.SQUISH_CONSTANT_4D;
} else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
dx_ext0 = dx0 - 1 - 2 * this.SQUISH_CONSTANT_4D;
dx_ext1 = dx_ext2 = dx0 - 1 - this.SQUISH_CONSTANT_4D;
}
if ((c & 0x02) == 0) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy0 - 2 * this.SQUISH_CONSTANT_4D;
dy_ext1 = dy_ext2 = dy0 - this.SQUISH_CONSTANT_4D;
if ((c & 0x01) == 0x01) {
ysv_ext1 -= 1;
dy_ext1 += 1;
} else {
ysv_ext2 -= 1;
dy_ext2 += 1;
}
} else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy0 - 1 - 2 * this.SQUISH_CONSTANT_4D;
dy_ext1 = dy_ext2 = dy0 - 1 - this.SQUISH_CONSTANT_4D;
}
if ((c & 0x04) == 0) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz0 - 2 * this.SQUISH_CONSTANT_4D;
dz_ext1 = dz_ext2 = dz0 - this.SQUISH_CONSTANT_4D;
if ((c & 0x03) == 0x03) {
zsv_ext1 -= 1;
dz_ext1 += 1;
} else {
zsv_ext2 -= 1;
dz_ext2 += 1;
}
} else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz0 - 1 - 2 * this.SQUISH_CONSTANT_4D;
dz_ext1 = dz_ext2 = dz0 - 1 - this.SQUISH_CONSTANT_4D;
}
if ((c & 0x08) == 0) {
wsv_ext0 = wsv_ext1 = wsb;
wsv_ext2 = wsb - 1;
dw_ext0 = dw0 - 2 * this.SQUISH_CONSTANT_4D;
dw_ext1 = dw0 - this.SQUISH_CONSTANT_4D;
dw_ext2 = dw0 + 1 - this.SQUISH_CONSTANT_4D;
} else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
dw_ext0 = dw0 - 1 - 2 * this.SQUISH_CONSTANT_4D;
dw_ext1 = dw_ext2 = dw0 - 1 - this.SQUISH_CONSTANT_4D;
}
}
//Contribution (0,0,0,0)
var attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;